The most common and most likely answer to this crossword clue is the 5 plus 4 letter word NEEDS MUST
I've seen this crossword clue in The Guardian
N
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S
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T
More clues leading to the result NEEDS MUST
- Muse tends to confuse — it’s inevitable
- Arithmetic: two poor grades in ten? Turning that round, it’s essential!
- Mused around at home? It’s necessary
- Shift dense smut – it’s a necessity
- Muse tends to get moving, when absolutely unavoidable
- Adolescent problems? Daughter accepted reverses couldn’t be helped
- Mend set eccentric American brought in? I can’t afford not to
- Requires grape juice for fermentation? That’s unavoidable
- Nut messed around as the occasion demands
- It’s inevitable Mumsnet loses head, going mad about Miliband and Balls?
Buddy explains!

The straight part
We know that "when absolutely unavoidable" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case when absolutely unavoidable = needs must.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.